Linearization of second-order reaction data

Reaction data described by the second‐order growth function A(t) = A∞(αt) (1 + αt)−1, where A∞ is the ultimate value of the product concentration A(t), can be linearized by plotting a suitable function F(t) against the time (t). The slope of the straight line obtained is (2α), where α is the product of the rate constant (k2) and the initial concentration of either reactant, with the result that k2 can be determined without knowledge of Aϰ. Optimal determination of the parameter α requires that data taking be limited to the interval 0 ≤ t ≤ T, where (αT) is approximately 4.0. Numerical data derived from an experiment on the exchange of lead by zinc ions in the enzyme carbonic anhydrase are analyzed to illustrate the method. The effects of small errors in the initial concentrations and of small deviations from second‐order kinetics are briefly discussed.